# «Research Division Federal Reserve Bank of St. Louis Working Paper Series Understanding the Accumulation of Bank and Thrift Reserves during the U.S. ...»

The third measure of all bad loans (bad loans, labeled “bad loans 3” in the regression tables) adds to nonperforming loans the full outstanding balances (not just delinquent payments) of loans and lease ﬁnancing receivables that are past due and on which the bank continues to accrue interest.19 Fig. 8 displays histograms of these three types of loans (nonaccruing, nonperforming, and all “bad” loans) as a percentage of total loans. Each graph plots the frequency of the ratios for the cross section of banks (top three graphs) and thrifts (bottom three graphs) at the beginning and end of our sample.20 The ﬁgures show quite strikingly the outward movement of the cross-sectional distribution of bad loans (in each category) between the beginning and the end of the sample window. During this period, the number of banks and thrifts with fewer distressed loans declined, and the number of banks and thrifts with 10 percent or more of their total loans classiﬁed as troubled increased markedly. These shifts are also consistent with the increase in bank and thrift failures during this period as a larger share of bad loans is correlated with the likelihood an institution will fail (see Aubuchon and Wheelock, 2010).

As a measure of capital adequacy, we use the equity-to-assets ratio adjusted in the numerator and denominator to remove intangibles (primarily goodwill). Intangibles show a strong positive trend due to mergers and acquisitions and in general are unable to absorb losses (see Lee and Stebunovs, 2012, for a discussion). We experimented 18 Loans and lease ﬁnancing receivables are reported as nonaccruing status if (i) they are maintained on a cash basis because of deterioration in the ﬁnancial position of the borrower or (ii) the principal or interest has been in default for a period of 90 days or more unless the obligation is both well secured and in the process of collection.

19 In particular, it includes closed-end monthly installment loans, lease ﬁnancing receivables, and open-end credit in arrears by two or three monthly payments; installment loans with payments scheduled less frequently than monthly when one scheduled payment is due and unpaid for 30 to 89 days; amortizing real estate loans after one installment is due and unpaid for 30 days to 89 days; single-payment and demand notes providing for payment of interest at stated intervals after one interest payment is due and unpaid for 30 days to 89 days; single-payment notes providing for payment of interest at maturity, on which interest or principal remains unpaid for 30 days to 89 days after maturity; unplanned overdrafts, whether or not the bank is accruing interest on them, if outstanding 30 to 89 days after origination.

20 We collect institutions with ratios larger than 15 (banks) and 10 (thrifts) in a unique bin.

with other measures of capital adequacy, including a measure of risk-weighted capital based on the ratio of Tier 1 capital to risk-adjusted assets. We report the results using the equity-to-assets ratio as this is a measure primarily determined by market rather than regulatory factors. For thrifts, we lack an adequate measure of equity holdings;

therefore, we use the ratio of Tier 1 capital to risk-adjusted assets as a measure of capital adequacy. We note that the eﬀect on ER of changes in Tier 1 capital for thrifts is therefore not directly comparable to the eﬀect of changes in the equity-to-assets ratio for banks due to our inability to control for the expectation of regulatory changes in Tier 1 capital.

Our ﬁnal measure of loan portfolio health is the ratio of loan loss provision to assets.

The loan loss provision is an income statement variable triggered by write-downs of the bank’s loan portfolio. When a loan loss provision is taken, the loan loss reserve must be rebuilt depending on the risk assessment of the remaining loan portfolio. The loan loss provision is an indicator of the extent to which a bank has removed nonperforming loans from its books.

We estimate a Tobit model, using the log of the ratio of ER and cash to deposits as the dependent variable and also taking the log of each of our independent quantity variables scaled by deposits.21 We include four key variables as regressors: a measure of the return to alternative investments, a measure of the penalty rate for holding insuﬃcient reserves, measures of the delinquency status of the loan portfolio (based on our three measures of distressed loans), and a measure of capital adequacy.

We run the same set of regressions using a censored least absolute deviations (CLAD) estimator model for data that admits a corner solution (see Powell, 1984).

The advantage of the CLAD estimator is that it is robust to heteroskedasticity and consistent and asymptotically normal for a variety of error distributions. As a quantile regression method, it is also not as sensitive to outliers as the Tobit model. We report results from Tobit and CLAD regressions below.

**4.2 Results**

In this section, we present the results from our Tobit and CLAD speciﬁcations. The log of the ratio of cash including ER (calculated as cash and reserve holdings 110 percent above required reserves) to deposits is the dependent variable. The regressions in Tables 3 and 4 report coeﬃcient estimates from Tobit and CLAD speciﬁcations with 21 We considered whether our problem could be better estimated using a Heckman selection model; see Section 5.2.4 for a discussion.

a left-censored value at zero; clustered (at the entity level) standard errors are listed in parentheses and all regressions include quarterly time dummies (not reported).22 4.2.1 All banks We ﬁrst look at Tobit and CLAD regressions for all banks (Table 3), second for banks by size (Tables 4 and 5), and third for thrifts (Table 6).23 We focus on the CLAD results for the reasons outlined above but note they are quite similar for the group of all banks.

Table 3 shows the diﬀerence between the 1-year Treasury bill rate and the interest rate paid on reserve balances at the Fed has a negative and signiﬁcant eﬀect on ER/cash accumulation, while the penalty rate has a positive and signiﬁcant eﬀect. These two eﬀects are as predicted by our theoretical model. When the opportunity cost of holding reserves rises, ceteris paribus, banks should reduce ER holdings. The fact that our regressions show that banks are sensitive to the opportunity cost of holding reserves suggests that the lack of alternative investment opportunities was not a frivolous motivation. Our estimation results imply that a 0.1 percent increase in the opportunity cost of holding reserves is consistent with a decrease in the ER plus cash-to-deposits ratio of 1 percent.

According to our model, when banks face heightened uncertainty about withdrawal rates, they will be more sensitive to movements in the penalty rate for having insuﬃcient reserves. For the regressions reported in Table 3, we use a daily index of Treasury bill repo rates, taking the last observation per quarter as a measure of the penalty rate. During our observation window (2008:Q3–2010:Q2), there was signiﬁcant disruption in the repo/reverse-repo market, which is a signiﬁcant source of short-term funding for banks. This disruption, which began with a 30 percent drop in federal funds and reverse-repo trading volumes in November 2008, recovered to some extent by April 2009, after which volumes again declined signiﬁcantly and continued to decline through the end of our sample. By 2010:Q2, the volume of trading in this market was only 36 percent of its value in 2008:Q3.

Not surprisingly, we ﬁnd ER and cash holdings respond strongly to increases in the penalty rate. For every 0.1 percent increase in the penalty rate, the ratio of ER and 22 The interpretation of the coeﬃcients on covariates measured in levels or ratios (the price variables and capital adequacy ratios) requires exponentiation of the coeﬃcients on the level covariates to obtain the eﬀect on the dependent variable, whereas the log-log speciﬁcation can be read as percentage changes from the tables.

23 The tables of Tobit results report the eﬀects of the covariates on the latent variable (observing positive ER) rather than the marginal eﬀects because the number of censored observations is suﬃciently small that the Tobit coeﬃcients approach their ordinary least squares counterparts so that the marginal eﬀects diﬀer from the reported results only at the fourth decimal place.

cash to deposits increases by approximately 5 percent. The strength of this response may also detect the reluctance of banks to provide negative market signals regarding their liquidity by borrowing in the overnight market during the ﬁnancial crisis (see Armantier et al., 2011; Gilbert et al., 2012). Maintaining cash and ER reduces banks’ reliance on the overnight market.

Next we turn to the impact of measures of bank health and loan performance on cash and reserves accumulation. Our measures of bank health are loan quality, provisions for loan losses, and the capital ratio. Bank capital ratios provide a measure of how adequately a bank is prepared for unexpected losses.

Our results on the eﬀect of capital adequacy are unstable across the Tobit and CLAD methods. Using the Tobit method, we ﬁnd that a 0.1 percent increase in capital adequacy (equity/assets) results in a 3.5 percent increase in ER and cash as a ratio to deposits, holding the loan loss provision at 0. Under the CLAD speciﬁcation, we ﬁnd that a similar increase is consistent with a 0.6 percent decrease in the ratio of ER and cash to deposits, holding the loan loss provision at zero. Although the eﬀects are small in both cases, we believe the CLAD results are more reliable. The total eﬀect of the capital ratio is the sum of its individual eﬀect (for the loan loss provision at zero) plus the coeﬃcient on the interaction times loan loss provision, exponentiating due to the semi-log format. We calculated the total eﬀect of a 1 percent increase in the capital ratio (based on the coeﬃcients in the CLAD regressions) to be -5.2 percent at the median level of loan loss provision, -4.4 at the 75th percentile, 0.03 percent at the 90th percentile, and 8.8 at the 95th percentile of loan loss provision. Banks with well-performing loan portfolios likely have low loan loss provisions and, therefore, higher capital adequacy translates into lower ER and cash accumulation. For banks burdened with large amounts of nonperforming and nonaccruing loans, increases in capital adequacy may be the result of reductions in assets due to write-downs rather than increases in equity, so higher capital adequacy results in more precautionary accumulation of reserves and cash. Another possibility is that banks with high loan loss provisions expect additional write-oﬀs in the near future so that higher capital adequacy is not entirely protective. Banks with fewer bad loans and a lower loan loss provision may have already cleaned their books and hence have lower capital and a lower capital ratio.24 These results also make sense of the coeﬃcient instability across speciﬁcations. Since the Tobit estimations are more sensitive to outliers, the coeﬃcients on the interaction 24 See Calomiris and Wilson (2004) for a discussion of this relationship during the Great Depression.

between capital adequacy and loan loss provision as well as loan loss provisions are likely unduly inﬂuenced by banks with large loan provisions (the standard deviation of loan loss provision is larger than the mean).

Evidence that this interpretation may be correct is provided by studying the total eﬀect of loan loss provisions, which equals the coeﬃcient on the ratio of loan loss provisions to assets (holding the capital ratio equal to zero) plus the coeﬃcient on the interaction between loan loss provisions and the capital ratio at various levels of the capital ratio. We ﬁnd the total eﬀect of a 0.1 percent increase in loan loss provision holding the capital ratio constant at the 50th percentile is a 4.1 percent increase in the ratio of ER and cash to deposits; at the 75th percentile, there is a 5.3 percent increase; at the 95th percentile, an 11 percent increase; and a 158 percent increase at the 99th percentile in the capital ratio. Banks with very high capital ratios (e.g., 99th percentile) possibly have such high ratios due to loan write-downs rather than large increases in equity. An increase in the loan loss provision at such a high ratio is consistent with a strong precautionary accumulation. Alternatively, these may be recently merged banks or banks with recent acquisitions. One last point is that there may also be tax considerations for the timing of loan loss provisions not considered here.

Our last group of the determinants of reserves accumulation is a set of three nested measures of bad loans, where the ﬁrst measure includes the most troubled loans (total nonaccruing), the second measure includes nonaccruing and adds nonperforming (90+ days late) loans, and the third measure includes the ﬁrst two bad loans measures plus loans between 30 and 90 days late. We ﬁnd all our measures have a similar eﬀect on ER and cash accumulation.25 We ﬁnd that a 1 percent increase in the ratio of bad loans to deposits results in a 0.3 percent increase in the ratio of ER and cash to deposits, suggesting a precautionary motive for accumulation.

In summary, ﬁrst, we ﬁnd evidence of precautionary accumulation by banks from the response of reserves and cash to the deterioration of their loan portfolio and the relationship between capital adequacy and loan loss provisions. Second, we ﬁnd banks are sensitive to the opportunity cost of holding low-interest-bearing assets, suggesting limited low-risk lending opportunities. Third, we ﬁnd banks are very sensitive to the penalty for holding insuﬃcient reserves in the event of a payment or withdrawal shock.

This result may be related to disruptions in the interbank and repurchase markets that 25 The fact that the standard errors are signiﬁcantly diﬀerent across the two methods suggests some heteroskedasticity in the residuals, though this does not aﬀect the coeﬃcient estimates.

occurred during our sample period.